Pencil and Paper Exercises on Sampling Statistics

1. The scores of individual students on the American College Testing
Program (ACT), a university admission exam, follow the normal 
distribution with mean of 18.6 and a standard deviation of 5.9
At one school 81 students participated in the test.  Determine the
expected mean (sample mean) and standard deviation (standard
error) of groups of 81 students.

2. The scores of individual students on the American College Testing
Program (ACT), a university admission exam, follow the normal 
distribution with mean of 18.6 and a standard deviation of 5.9
  (a) What is the chance that a randomly selected student 
     scores 21 points or higher?
  (b) The class average of one class of 81 students was m=20.4
     What is the chance that the average of a randomly chosen
     group of 81 students would be 20.4 or higher.

3. In one experiment on reading ability two techniques are compared, A
and B.  The variable to be predicted is the reading score known as
'Degree of Reading Power'(DRP).  The researcher used method A in a
group of 25 pupils and method B in a second group of 16 pupils.
Pupils were randomly assigned to one or the other group.  Assume that
the population of all children of the relevant age follows a N(34,10)
distribution in the case of method A, and a N(37,12) distribution in
the case of method B.
  (a) What is distribution of the average DRP scores for method A in
     groups of 25 pupils?   Assume that these group may be viewed
     as randomly selected samples.
  (b) What is the distribution of average scores for method B in
     groups of 16 pupils.